RF SR: What If I'm Anchored to a Moving Train?

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SUMMARY

This discussion centers on the concept of time dilation as observed between two reference frames (RFs): one anchored to the ground and another anchored to a moving train (S'). In this scenario, both observers perceive the other's clocks as moving slower due to their relative velocities. The phenomenon is a direct consequence of the principles of special relativity, where high-speed motion affects the passage of time and the measurement of lengths (length contraction). Both reference frames are equally valid, highlighting the relativity of simultaneity and the nature of time in physics.

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What if I am in a RF, S, anchored to the ground, and there is another RF S', which is anchored to a train. According to my RF, the clocks in the train moves slower, but according to S', does my clocks move slower too?
 
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Yup, and by exactly the same amount. Likewise, you see rulers on the train shrunk relative to your rulers, and an observer on the train sees your rulers shrunk relative to rulers on the train.
 


In this scenario, your clocks in your RF will appear to move at a normal pace, but from the perspective of S', they will appear to be moving slower. This is due to the concept of time dilation, where time appears to move slower for objects in motion relative to an observer. So, in your reference frame, your clocks will appear to be moving at a normal pace, but in the reference frame of S', your clocks will appear to be moving slower. This is because the train is moving at a high velocity, causing time to appear to pass slower for objects within it. Therefore, your clocks will appear to be moving slower from the perspective of S'. However, it is important to note that both reference frames are equally valid, and time dilation is a relative concept.
 

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